Asymptotics for fractional reaction diffusion equations in periodic media
In this paper, the Cauchy problem for a class of reaction diffusion equations are considered with nonlocal interactions in periodic media. First, we demonstrate the existence and uniqueness of solutions that are both positive and bounded for the stationary equation. Second, we derive results concern...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-02-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025177 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850216310916513792 |
|---|---|
| author | Yu Wei Yahan Wang Huiqin Lu |
| author_facet | Yu Wei Yahan Wang Huiqin Lu |
| author_sort | Yu Wei |
| collection | DOAJ |
| description | In this paper, the Cauchy problem for a class of reaction diffusion equations are considered with nonlocal interactions in periodic media. First, we demonstrate the existence and uniqueness of solutions that are both positive and bounded for the stationary equation. Second, we derive results concerning the existence and uniqueness of solutions for the Cauchy problem by using the semigroup theory. Finally, we analyze the behavior of the solutions to the Cauchy problem for large times by using the comparison principle. |
| format | Article |
| id | doaj-art-f0a0890398d54be98d3f034da2fb2fa0 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-f0a0890398d54be98d3f034da2fb2fa02025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-02-011023819383510.3934/math.2025177Asymptotics for fractional reaction diffusion equations in periodic mediaYu Wei0Yahan Wang1Huiqin Lu2School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, ChinaIn this paper, the Cauchy problem for a class of reaction diffusion equations are considered with nonlocal interactions in periodic media. First, we demonstrate the existence and uniqueness of solutions that are both positive and bounded for the stationary equation. Second, we derive results concerning the existence and uniqueness of solutions for the Cauchy problem by using the semigroup theory. Finally, we analyze the behavior of the solutions to the Cauchy problem for large times by using the comparison principle.https://www.aimspress.com/article/doi/10.3934/math.2025177generalized fractional laplacianconvolutionsemigroup theoryasymptotics |
| spellingShingle | Yu Wei Yahan Wang Huiqin Lu Asymptotics for fractional reaction diffusion equations in periodic media AIMS Mathematics generalized fractional laplacian convolution semigroup theory asymptotics |
| title | Asymptotics for fractional reaction diffusion equations in periodic media |
| title_full | Asymptotics for fractional reaction diffusion equations in periodic media |
| title_fullStr | Asymptotics for fractional reaction diffusion equations in periodic media |
| title_full_unstemmed | Asymptotics for fractional reaction diffusion equations in periodic media |
| title_short | Asymptotics for fractional reaction diffusion equations in periodic media |
| title_sort | asymptotics for fractional reaction diffusion equations in periodic media |
| topic | generalized fractional laplacian convolution semigroup theory asymptotics |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025177 |
| work_keys_str_mv | AT yuwei asymptoticsforfractionalreactiondiffusionequationsinperiodicmedia AT yahanwang asymptoticsforfractionalreactiondiffusionequationsinperiodicmedia AT huiqinlu asymptoticsforfractionalreactiondiffusionequationsinperiodicmedia |